Is there a way to make different HDRIs be reflected on specific objects in the same render?
Would be helpful if you can closer describe what exactly you want to achieve by this technique.

If you want to affect one object by one HDRi and second object by another HDRi from World shader - you can't (from what I know). From World shader you can use more HDRi to affects different types of light rays with Light path node. That is what you mentioned already I guess. Those affects all objects in a scene. For something like that you would have to render twice and merge in compositor.
In some cases you can fake few things like reflection per object on material level.
Like here is used another HDRi for reflection.

Tip: Quite great explanation of &quot;Light Path&quot; node.